On the Bloch-Kato conjecture for GSp(4)

Abstract

We prove an explicit reciprocity law for the Euler system attached to the spin motive of a genus 2 Siegel modular form. As consequences, we obtain one inclusion of the Iwasawa Main Conjecture for such motives, and the Bloch--Kato conjecture in analytic rank 0 for their critical twists.

Accepted version, to appear in "Cambridge J. Math."

References in corpus (9)

• Single-valued integration and superstring amplitudes in genus zero
• Euler systems for GSp(4)
• Higher Hida theory and p-adic L-functions for GSp(4)
• Single-valued integration and double copy
• Local Whittaker-Newforms for GSp(4) matching to Langlands parameters
• $L$-functions of $\mathrm{GL}(2n):$ $p$-adic properties and non-vanishing of twists
• Syntomic regulators of Asai--Flach classes
• Comparison between rigid syntomic and crystalline syntomic cohomology for strictly semistable log schemes with boundary
• Spinor Euler factors for GSp(4) in the subregular case

Cited by in corpus (14)

• P-adic L-functions and diagonal cycles for GSp(4) x GL(2) x GL(2)
• On local zeta-integrals for GSp(4) and GSp(4) x GL(2)
• On some zeta-integrals for unramified representations of GSp(4)
• On the Bloch--Kato conjecture for GSp(4) x GL(2)
• On p-adic regulators for GSp(4) x GL(2) and GSp(4) x GL(2) x GL(2)
• On the Bloch--Kato conjecture for the symmetric cube
• Iwasawa theory for quadratic Hilbert modular forms
• Hirzebruch-Zagier classes and rational elliptic curves over quintic fields
• Special cycles on orthogonal Shimura varieties
• On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces
• Higher Hida theory for Hilbert modular varieties in the totally split case
• Iwasawa theory of automorphic representations of ${\mathrm{GL}}_{2n}$ at non-ordinary primes
• Poincaré duality for rigid analytic Hyodo--Kato theory
• Explicit Motivic Mixed Elliptic Chabauty-Kim